Thermodynamics of Natural Systems

657 Pages·2005·2.76 MB·English

by  G. M. Anderson

Thermodynamics of Natural Systems
Second Edition
Thermodynamics deals with energy levels and the transfer of energy between
states of matter, and is therefore fundamental to many branches of science.
This new edition provides a relatively advanced treatment of the subject,
specifically tailored to the interests of the Earth sciences.
The first four chapters explain all the necessary concepts of thermodynamics,
using a simple graphical approach. Throughout the rest of the book the author
emphasizes the use of thermodynamics to construct mathematical simulations
of real systems. This helps to make the many abstract concepts accessible.
Many computer programs are mentioned and used throughout the text,
especially SUPCRT92, a widely used source of thermodynamic data. Links to
useful information sites and computer programs as well as problem sets with
detailed answers for instructors are available through
http://www.cambridge.org/0521847729.
Building on the more elementary material in the first edition, this textbook
will be ideal for advanced undergraduate and graduate students in geology,
geochemistry, geophysics and environmental science.
Greg Anderson has been Professor of Geochemistry at the University of
Toronto for 35 years and is the author of three textbooks on thermodynamics
for Earth scientists: Environmental Applications of Geochemical Modeling
(2002), Thermodynamics in Geochemistry (1993) and Thermodynamics of
Natural Systems (1995). In 2000 he was awarded the Past President’s Medal
bytheMineralogicalAssociationofCanadaforcontributionstogeochemistry.
Thermodynamics of
Natural Systems
Second Edition
G. M. Anderson
University of Toronto
  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
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Contents
Preface Pagexiii
1 Whatisthermodynamics? 1
1.1 Introduction 1
1.2 What is the problem? 1
1.3 A mechanical analogy 2
1.4 Limitations of the thermodynamic model 6
1.5 Summary 6
2 Definingourterms 8
2.1 Something is missing 8
2.2 Systems 8
2.3 Equilibrium 12
2.4 State variables 17
2.5 Phases and components 20
2.6 Processes 21
2.7 Summary 28
3 Thefirstlawofthermodynamics 31
3.1 Temperature and pressure scales 31
3.2 Internal energy 32
3.3 Energy transfers 35
3.4 The first law of thermodynamics 37
3.5 Enthalpy, the heat of reaction 46
3.6 How far have we got? 61
3.7 The model again 61
3.8 Summary 63
4 Thesecondlawofthermodynamics 65
4.1 Introduction 65
4.2 The problem restated 65
4.3 Thermodynamic potentials 66
4.4 Entropy 67
4.5 The fundamental equation 74
vii
viii Contents
4.6 The USV surface 75
4.7 Those other forms of work 77
4.8 Applicability of the fundamental equation 78
4.9 Constraints and metastable states 79
4.10 The energy inequality expression 83
4.11 Entropy and heat capacity 85
4.12 A more useful thermodynamic potential 91
4.13 Gibbs and Helmholtz functions as work 94
4.14 Open systems 97
4.15 The meaning of entropy 103
4.16 A word about Carnot 107
4.17 The end of the road 107
4.18 Summary 108
5 Gettingdata 111
5.1 Introduction 111
5.2 What to measure? 112
5.3 Solution calorimetry 115
5.4 The third law 119
5.5 The problem resolved 125
5.6 Data at higher temperatures 133
5.7 Data at higher pressures 141
5.8 Other methods 145
5.9 Summary 149
6 Somesimpleapplications 150
6.1 Introduction 150
6.2 Some properties of water 150
6.3 Simple phase diagrams 161
6.4 The slope of phase boundaries 165
6.5 Another example 171
6.6 Summary 175
7 Idealsolutions 176
7.1 Introduction 176
7.2 Measures of concentration 177
7.3 Properties of ideal solutions 180
7.4 Ideal solution laws 182
7.5 Ideal solution equations 187
7.6 Next step – the activity 196
7.7 Summary 196
8 Fugacityandactivity 198
8.1 Fugacity 198
8.2 Activity 206
Contents ix
8.3 Standard states and activity coefficients 211
8.4 Effect of temperature and pressure on activities 224
8.5 Activities and standard states: an overall view 227
8.6 Summary 233
9 Theequilibriumconstant 234
9.1 Reactions in solution 234
9.2 Reactions at equilibrium 236
9.3 The most useful equation in thermodynamics 237
9.4 Special meanings for K 242
9.5 K in solid–solid reactions 250
9.6 Change of K with temperature I 252
9.7 Change of K with temperature II 257
9.8 Change of K with pressure 264
9.9 The amino acid example again 265
9.10 Some conventions regarding components 269
9.11 Summary 273
10 Realsolutions 274
10.1 Introduction 274
10.2 Solution volumes 274
10.3 The infinite dilution standard state 284
10.4 Excess properties 287
10.5 Enthalpy and heat capacity 293
10.6 Gibbs energies 302
10.7 Margules equations 310
10.8 Beyond Margules 313
10.9 The Gibbs–Duhem equation 314
10.10 Summary 316
11 Thephaserule 317
11.1 Introduction 317
11.2 Derivation of the phase rule 317
11.3 Components and species 321
11.4 Duhem’s theorem 326
11.5 Buffered systems 330
11.6 Summary 334
12 Redoxreactions 335
12.1 Introduction 335
12.2 Electron transfer reactions 335
12.3 The role of oxygen 336
12.4 A simple electrolytic cell 338
12.5 The Nernst equation 341
12.6 Some necessary conventions 344
x Contents
12.7 Measuring activities 347
12.8 Measuring redox conditions 349
12.9 Eh–pH diagrams 354
12.10 Oxygen fugacity 359
12.11 Redox reactions in organic chemistry 362
12.12 Summary 363
13 Equationsofstate 366
13.1 Introduction 366
13.2 The ideal gas 366
13.3 Two kinds of EoS 371
13.4 Cubic equations of state 371
13.5 The virial equation 378
13.6 Thermal equations of state 384
13.7 Other equations of state 391
13.8 Summary 394
14 Solidsolutions 395
14.1 Introduction 395
14.2 Solid solutions 396
14.3 Activity coefficients in solid solutions 403
14.4 Summary 420
15 Electrolytesolutions 422
15.1 Introduction 422
15.2 Activities of electrolyte components 422
15.3 Numerical values for single-ion properties 436
15.4 The Debye–Hückel theory 440
15.5 Activity coefficients of neutral molecules 447
15.6 Ion association, ion pairs, and complexes 449
15.7 The Pitzer equations 451
15.8 The HKF model for aqueous electrolytes 461
15.9 Comparison of Pitzer and HKF models 471
16 Rock–watersystems 473
16.1 Real problems 473
16.2 Is the sea saturated with calcium carbonate? 473
16.3 Determining the IAP – speciation 477
16.4 Combining the IAP and the K 484
sp
16.5 Mineral stability diagrams 487
16.6 Summary 497
17 Phasediagrams 499
17.1 What is a phase diagram? 499
17.2 Unary systems 500
17.3 Binary systems 507
Contents xi
17.4 Ternary systems 533
17.5 Summary 540
18 Processmodeling 542
18.1 Introduction 542
18.2 Kinetics 543
18.3 Using the progress variable 550
18.4 Affinity and the progress variable 562
18.5 Final comment 572
Appendices
A Constantsandnumericalvalues 574
B Standardstateproperties 576
C Somemathematics 586
C.1 Essential mathematics 586
C.2 Nonessential mathematics 590
D Howtousesupcrt92 601
E Computerprograms 605
E.1 FORTRAN 605
E.2 matlab 612
F Symbolsused 617
F.1 Variables 617
F.2 Superscripts 618
F.3 Subscripts 618
F.4 Comments on nonIUPAC usage 618
G Ashorthistoryofthermodynamicconstraints 620
G.1 Introduction 620
G.2 Schottky et al. (1929) 620
G.3 Tisza (1966) 622
G.4 Callen (1960) 622
G.5 Reiss (1965) 623
G.6 Weinreich (1968) 625
G.7 Summary 625
References 627
Index 641
1
What is thermodynamics?
1.1 Introduction
Thermodynamicsisthebranchofsciencethatdealswithrelativeenergylevels
andtransfersofenergybetweensystemsandbetweendifferentstatesofmatter.
Becausethesesubjectsariseinvirtuallyeveryotherbranchofscience,thermo-
dynamics is one of the cornerstones of scientific training. Various scientific
specialties place varying degrees of emphasis on the subject areas covered
by thermodynamics – a text on thermodynamics for physicists can look quite
differentfromoneforchemists,oroneformechanicalengineers.Forchemists,
biologists,geologists,andenvironmentalscientistsofvarioustypes,thethermo-
dynamics of chemical reactions is of course a central concern, and that is the
emphasis to be found in this book. Let us start by considering a few simple
reactions and the questions that arise in doing this.
1.2 What is the problem?
1.2.1 Some simple chemical reactions
A chemical reaction involves the rearrangement of atoms from one structure
orconfigurationtoanother,normallyaccompaniedbyanenergychange.Let’s
consider some simple examples.
•
Take an ice cube from the freezer of your refrigerator and place it in a cup on the
counter.Afterafewminutes,theicebeginstomelt,anditsooniscompletelychanged
towater.Whenthewaterhaswarmeduptoroomtemperature,nofurtherchangecan
be observed, even if you watch for hours. If you put the water back in the freezer,
it changes back to ice within a few minutes, and again there is no further change.
Evidently, this substance (H O) has at least two different forms, and it will change
2
spontaneouslyfromonetotheotherdependingonitssurroundings.
•
Take an egg from the refrigerator and fry it on the stove, then cool to room tem-
perature. Again, all change seems now to have stopped – the reaction is complete.
However,puttingthefriedeggbackintherefrigeratorwillnotchangeitbackintoa
rawegg.Thischangeseemsnottobereversible.Whatisdifferentinthiscase?
1